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1) Firstly, let's check out the prime factorization of 171! We observe that the sum of digits add up to 1+7+1=9. Hence, 9 is a factor of 171. From there, we can deduce that 171=3x3x19.

We haven't got many submissions for Carnival #171. One of them is from Mr Zor Shekhtman:

2)
By now UNIZOR.COM has about 1000 lectures. The course "Math 4 Teens" is finished (though, a few exams might be added). I am working now on the new course "Physics 4 Teens". Completed the "Mechanics" part and working now on "Energy". There about 1500 followers to my YouTube channel.

Do check out the above website if you are interested in videos and courses on Maths and Physics.

3)
A great part of mathematics is psychological, to be specific, resilience is very important. Never giving up is the key to success. The AMS and MAA have recently published (and made available online) a collection of essays entitled “Living Proof: Stories of Resilience Along the Mathematical Journey”. Each author contributes a story of how they encountered some internal or external difficulty in advancing their mathematical career, and how they were able to deal with such difficulties. More details are available on Professor Terence Tao's website: https://terrytao.wordpress.com/2019/06/27/living-proof-stories-of-resilience-along-the-mathematical-journey/
Do check it out if you need some additional motivation in your mathematical journey.

4)
I would like to recommend Joseph Nebus' blog: https://nebusresearch.wordpress.com/. If you haven't already done so, do check it out! It is full of interesting mathematical tidbits like comics, and expository essays targeting the general audience, for example his "A to Z" series of essays.

6)
For an alternative proof that the square root of 2 is irrational, check out this post. It can be said to be a more "constructive" approach than the popular proof by contradiction, though some may argue that it is not the case.

7)
For more advanced readers, you may want to check out this post on Fermat's Two Squares Theorem. It explains why certain numbers can be expressed as the sum of two squares, for instance 13=2^2+3^2.

8)
Lastly, let's end off with a Math video, with the highly popular and recommended channel 3Blue1Brown. It is on the very hot topic of Neural Networks:

Welcome to the Playful Math Education Carnival #125! I will try my best to include some interesting math education posts!

1) For many homeschool kids, chess can be an interesting hobby. This latest video by Numberphile explains nicely the Elo rating system for chess (and other games).

4) Everyone loves a riddle, especially one that is tricky but only involves elementary mathematics! This horse riddle can theoretically be solved by a first grader, but yet has stumped many adults! Check out the horse riddle here: https://mathtuition88.com/2018/02/19/tricky-riddle-involving-a-horse/

6) Denise Gaskins, the founder of Playful Math Education Carnival, has posted a quote on "Math is Like a Nature Walk". Being a nature lover and a math lover, I totally agree with the quote. Do check it out!

7) I also enjoyed reading this blog post by Jessica Roberts on the curriculum (including Math) she uses to homeschool her 5 (if I counted correctly) kids! (Update: She actually has 7 kids!)

8) Recently, my new hobby is keeping fish. Being a Math lover, I was naturally curious if fish can count? Check out the surprising answer here. (To let the cat out of the bag, scientists found that fish can count up to four - but no higher. I believe this may be an understatement, some fish are quite intelligent indeed.)

9) I would also like to recommend Joseph Nebus' blog, NebusResearch. His blog features mathematical cartoons, and also explains mathematics to laypeople in a highly interesting and accessible manner. Do check out his A to Z series, they are very well written.

10) The last topic is on Machine Learning (possibly for more advanced high school students). Machine Learning is the latest hype and it has produced a lot of excellent results in the realm of artificial intelligence. It is good for students to just get to know a bit of it, and the general idea of what Machine Learning is all about. Hopefully it will pique their interest!

Note: If you want to deal with hexadecimal numbers (base 16), add a '0X' (Zero, not O) in front of the number. Eg: "FF" becomes "0XFF"!
Try not to use extremely large numbers unless your computer's speed is over 2000 mHz! The largest base you should use is 40, which is quite large already. You can also use bases larger than 40 but sometimes they won't work...

To multiply a number in a certain base, just convert the numbers into base 10 first, then convert them back into the required base!

We have written a 3000 word comprehensive article about What is Singapore Math, including book recommendations.

Singapore Math is widely used in the United States, in the states of California, Massachusetts, Washington, Maryland and more. It is also used in France and even Chile.

The benefits of Singapore Math include developing critical mathematical and logical thinking skills to solve higher-order math problems.

Do check out the Recommended Singapore Math books at the end of the article, they represent the best and most popular Singapore Math books in the market.